WO2001077734A1

WO2001077734A1 - Compact imaging system including an aspheric quaternary element

Info

Publication number: WO2001077734A1
Application number: PCT/NZ2001/000053
Authority: WO
Inventors: Allan David Beach
Original assignee: Industrial Research Limited
Priority date: 2000-04-07
Filing date: 2001-04-06
Publication date: 2001-10-18
Also published as: AU2001252787A1

Abstract

An imaging system (100) is provided that includes a primary mirror (1), secondary mirror (2), tertiary mirror (3) and quaternary mirror (4) arranged in a single-axis, double-pass, four reflection format. The quaternary mirror (4) is an aspheric reflecting element. The quaternary mirror (4) may be substantially planar and the primary, secondary and tertiary mirrors (1, 2, 3) may be arranged in a Cassegrain-like format.

Description

COMPACT IMAGING SYSTEM INCLUDING AIM ASPHERIC QUATERNARY ELEMENT

TECHNICAL FIELD

This invention relates to a compact imaging system and in particular, but not exclusively to a compact imaging system suitable for efficient transportation.

The present invention may have particular application to the imaging of objects at long distances by telescopes and cameras, although other applications including but not limited to terrestrial surveillance is anticipated.

BACKGROUND

Optical imaging systems are used for a wide variety of applications including astronomy, surveillance, measurement, projection of information and a variety of other applications.

With respect to astronomical applications, as telescope and camera technology has advanced, improved images of the universe have been obtainable. However, a limiting factor has always been the presence of interfering light from the numerous light sources on Earth and the distorting effects of the Earth's atmosphere. Therefore, astronomers are now looking at placing telescopes into orbit to overcome these problems.

In order to place a telescope into orbit, it has to be transported by rockets or a shuttle to the required height above the Earth's surface and released into a sustainable orbit. The cost of transporting objects into space is invariably high and typical costs at present may be around US$ 1 0,000.00 per kilogram mass. Also, there is a significant cost per unit volume. Therefore, there is a need for relatively short, light optical systems in relation to their diameter to allow more cost-effective transportation into space. It will be appreciated that terrestrial transportation is also cheaper with smaller, lighter systems, the marginal cost just not as high.

Generally in conflict with the requirements for shorter, lighter structures, are the requirements to produce an imaging system which possess high quality imaging characteristics. In particular, the optical imaging system should generate an image of a usefully large object field and have a high, ideally diffraction-limited, angular resolution over this entire field. Furthermore, the speed of the system should be such that the diffraction blur is comparable with the detector pixel dimensions to fully take advantage of the useable diffraction limited performance available in space. The spectral pass-band should be limited only by the available materials; sufficient baffling should be included against the entrance of stray light into the system and the system should have a flat focal surface to match that of the detector device.

Advances in optical manufacturing technology have resulted in the reduction of practical fabrication limitations on imaging systems. Numerically controlled diamond turning of glass, together with computer-controlled conformable lapping, has made the creation of previously "difficult" aspheric optical surfaces less of a costly problem. Also new materials, such as low thermal-expansion glass ceramics, have eliminated environmental temperature variation problems that were once a limiting factor. Furthermore, advanced tolerancing software has enabled practical manufacturing constraints to be included in the design process and optimisation algorithms are continually being improved. Practical solutions to the above problems require single-axis designs on the basis that multi-axis designs are structurally complex and hence more costly and prone to damage in high speed transportation. Catadioptric solutions are typically also excluded due to the spectral passband constraints caused by the dispersive refractivity of dioptric components. This is in contrast to ground-based systems that are subject to atmospheric spectral pass-band constraints and in which refractive components are necessarily included to compensate for the prismatic effect of the atmosphere when the telescope is directed substantially away from the zenith.

Three-mirror, three reflection systems typically result in an undesirable image position, being either forward of, or between the primary and secondary mirrors and generated by forward-propagating light rays. This requires complex electronic systems on and around the detector, as well as filter changing devices and other mechanical modules that tend excessively to obscure the central region of the entrance pupil. This is in contrast to four reflection designs where the image is located rearward of the primary mirror and generated by rearward-propagating light rays.

However, existing four-mirror designs are typically structurally complex and/or slow and generally have failed to take advantage of the improved characteristics of three-mirror systems prior to reflecting off the fourth mirror.

Thus, it is an object of the present invention to provide an imaging system which overcomes or at least alleviates problems in imaging systems at present, or at least one which provides the public with a useful choice. Further objects the present invention may become apparent from the following description

SUMMARY OF THE INVENTION

According to one aspect of the present invention, there is provided an imaging system including a primary, secondary, tertiary and quaternary mirror arranged in a single-axis, double-pass, four reflection format, wherein the quaternary mirror is an aspheric reflecting element.

Preferably, the primary, secondary and tertiary mirrors are collectively arranged in a Cassegrain-hke format

Preferably, the primary and tertiary mirrors are monolithic.

Preferably, the primary, secondary and tertiary mirrors have a reflecting surface that is substantially hyperboloidal.

Preferably, the tertiary mirror includes an aspheric form superimposed on its surface to reduce aberrations in an image and the primary and secondary mirrors do not have a superimposed aspheric form.

Preferably, the tertiary mirror and the primary mirror both include an aspheric form superimposed on their respective reflecting surfaces to reduce aberrations in an image and the secondary mirrors does not include a superimposed aspheric form.

Preferably, the quaternary mirror has a radius of curvature substantially greater than the radius of curvature of the primary, secondary and tertiary mirrors.

Preferably, the quaternary mirror has a radius of curvature tending towards infinity relative to the curvature of the primary, secondary and tertiary mirrors.

Preferably, the physical length of the imaging system is approximately equal to or less than the diameter of the entrance pupil.

Preferably, the quaternary mirror is adapted to reduce aberrations in the image.

Preferably, the quaternary mirror is adapted to provide zonal corrections to the image.

Preferably, the imaging system further includes a baffle extending from the periphery of the primary mirror towards or past the secondary mirror.

Preferably, the imaging system further includes a baffle located centrally of the tertiary mirror and about the image focal point of the imaging system.

Preferably, the imaging system includes an aperture stop located substantially at the physical location of the primary mirror.

Preferably, the imaging system includes an aperture stop located substantially in a plane coterminous with the secondary mirror.

Preferably, the relative diameters and location of the primary, secondary, tertiary and quaternary mirrors are such that in use only the secondary mirror acts to obscure the central part of the pupil at any field angle.

Preferably, the imaging system has a speed faster than or equal to f/2.5.

According to another aspect of the present invention, there is provided a method of imaging light onto an image detecting means including: - receiving incident light by a primary mirror; reflecting light from said primary mirror using a secondary mirror; reflecting light from said secondary mirror using a tertiary mirror located substantially on a common axis to said primary and secondary mirrors; - reflecting light from said tertiary mirror using an aspheric quaternary mirror located substantially on said common axis; and receiving light from said quaternary mirror by an image detecting means.

According to a further aspect of the present invention, there is provided a method of designing an imaging system that includes a primary, secondary, tertiary and quaternary mirror in a single-axis, double-pass, four reflection format, the method including computing an imaging solution that satisfies a set of predetermined criteria using an optimisation algorithm that includes as variables: the relative location and curvature of said primary, secondary, tertiary, and quaternary mirror along said axis; and the structure of an aspheric form superimposed over said quaternary mirror.

Preferably, the method includes using the structure of an aspheric form superimposed over said tertiary mirror as a further variable.

Preferably, the method includes using the structure of an aspheric form superimposed over said primary mirror as a further variable.

Preferably, the radius of curvature of the quaternary mirror is constrained so that the quaternary mirror is substantially planar relative to the primary, secondary and tertiary mirrors.

Preferably, the radius of curvature of the quaternary mirror is infinite.

According to another aspect of the present invention, there is provided an imaging system designed in accordance with the method herein above described.

Further aspects of the present invention may become apparent from the following description, which is given by way of example only, and in which reference is made to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGURE 1 : Shows an example of a prior art Rumsey imaging system;

FIGURES 2, 4, 6, 8: Show a diagrammatic representation of four examples of an imaging system according to the present invention; FIGURES 3, 5, 7, 9: Show computed imaging results of the imaging systems of Figures 2, 4, 6 and 8.

FIGURE 10: Shows a graph of the simulated results of the field angle versus pupil diameter for a

Strehl Ratio 0.9.

DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

First, referring to Figure 1 , a schematic representation of a prior art imaging system is shown. This system, typically referred to as a Rumsey 3-mirror system, includes a primary mirror A, a secondary mirror B and a tertiary mirror C. The focal plane D is located forward of the secondary mirror B. The light rays E are reflected three times within the system before being focussed at the focal plane D. A mechanical advantage of the Rumsey system is that the tertiary mirror is monolithic with the primary, and its surface is contiguous with the primary's surface and has a steeper gradient at the common zonal radius, thus enabling relatively simple fabrication and mounting. In space operations, it is a major advantage that no additional supporting structures are needed for the tertiary mirror C as such supporting structures add weight to the imaging system. In the Rumsey imaging system, the tertiary mirror may be designed independently from the primary mirror, depending on the specific requirements of the imaging system.

Example 1

Referring now to Figure 2, a diagrammatic representation of a first example of an imaging system according to the present invention is shown and generally referenced by arrow 100. The primary mirror 1 , secondary mirror 2 and tertiary mirror 3 are configured in a similar arrangement to the Rumsey imaging system shown in Figure 1 and have substantially hyperboloidal reflecting surfaces United States Patent Number 3,460,886 describes the Rumsey imaging system and is incorporated in its entirety herein by reference where appropriate.

Accordingly, the primary, secondary and tertiary mirrors 1 , 2, 3 respectively are arranged in a similar format to a Cassegrain imaging system, in particular a double-pass Cassegrain imaging system. A quaternary mirror 4 is added to the system to receive and reflect light from the tertiary mirror 3. However, it will be appreciated by those skilled in the art that variations from Cassegrain- ke systems may be implemented without departing from the scope of the invention, the preferred system having a single-axis, double-pass four reflection format The Cassegrain-hke arrangement has the advantage of resulting in a particularly compact imaging system, is fast and has a relatively wide useful field angle

The quaternary mirror 4 is located between the reflecting element containing the primary mirror 1 and the tertiary mirror 3, and the secondary mirror 2 By adding the quaternary mirror 4, the image- forming light is directed rearwards, thus enabling a less constrained mechanical arrangement for electronics, filter-changing devices and other functional modules known in the art, that may obscure the image- forming light if located in front of, or between the mirrors.

The quaternary mirror 4 can be used to emulate the function of the well known "Gascoigne plate" to inter alia provide zonal corrections to the image forming light rays. Therefore, the quaternary mirror 4 is asphencal The quaternary mirror 4 may be substantially "flat" or "zero powered" in that it has a radius of curvature tending towards infinity relative to the primary mirror or, in some design configurations, it may be slightly convex or concave if extra degrees of freedom are required in the design process. The first four coefficients A2 to A8 of the standard aspheric function z, shown in equation 1 , were used as design variables for the imaging system.

^{Cr ~} _{ι +} (A2 ₊ (A4 ₊ (A6 ₊ (A8)r ...._equat,on 1

] + - (\ + k)c^~r-

Where z is the surface deformation, c is the curvature, r is the radial coordinate and k is the conic constant.

Those skilled in the art will be aware that to design an imaging solution to meet a set of requirements, an computational algorithm is typically the most convenient method of establishing the variables the system. Once the general form of the system is known, the computational algorithm may compute the imaging results for variations of predetermined variables These predetermined variables typically include the relative locations of each element within the imaging system, the curvature of the components and the type of materials used for each component. Furthermore, for imaging systems including one or more elements with an aspheric form superimposed thereon, the structure of the aspheric form(s) is a further variable requiring computation.

When designing a system according to the present invention, the computational algorithm is constrained to work with a single axis, double pass, four reflection format. The curvature of the quaternary mirror may be constrained to be planar, or slight curvatures may be permitted. Due to the number of possible variations, there may be an almost infinite number of different imaging systems which satisfy any single set of performance criteria.

It will be appreciated by those skilled in the art, that the inclusion of an extra mirror (quaternary mirror 4) may create some loss in light within the system due to imperfect reflection. However, the extra mirror also provides further degrees of freedom in designing the imaging system. Therefore, improved imaging properties may be achieved in the system optimisation process than would otherwise be available in systems based more closely on the Rumsey imaging system.

As a result, the inclusion of the quaternary mirror 4 allows a substantial increase in speed and reduction in the length of the imaging system for a given pupil diameter, while retaining high levels of aberration correction. For example, the imaging system 100 shown in Figure 2 has a pupil diameter of 500 mm and a speed of f/2.4, whereas in contrast, the Rumsey system shown in Figure 1 has a lesser pupil diameter of 300 mm and a lower speed of f/5.

The more compact arrangement of the imaging system 100 means that the length of the system may be designed to be comparable to the diameter of the pupil. Therefore, the imaging system 100 has a significantly reduced volume over known imaging systems having similar properties and, therefore, is ideally suited to transportation where the cost per unit volume is high.

Slower imaging systems could also be designed in accordance with the present invention for example, if a wider field angle is required. It will be appreciated by those skilled in the art that slower systems will have a slightly increased length, but the overall system is still more compact than existing systems having an equivalent speed.

Tubular baffles 5 and or 5a may be included to exclude stray light from directly entering the system's front aperture 6 and impinging on the focal surface 7. This reduces interference from light sources outside the field of view and located around the imaging system.

Table 1 lists the physical characteristics of a 500 mm diameter imaging system designed according to the present invention. The surfaces 1 to 4 correspond to the mirrors referenced 1 to 4 respectively in Figure 2. The radius of curvature of each surface is shown in the second column. The image has an infinite radius of curvature, which is a requirement for most practical image detectors at present. The size of the overall system is primarily dictated by the distance between the surfaces. The distance between surface 1 and surface 2 is relatively small in comparison to the diameter of the primary mirror 1 (surface 1 ), allowing the imaging system of the present invention to have a length comparable with, or less than its pupil diameter. The conic constant of each mirror is given in column 6, showing that the primary, secondary and tertiary mirrors in this embodiment are all hyperboloids with increasing conic constant. Further shown in table 1 is a set of optimally computed aspheric coefficients from equation 1 for the aspheric form of the quaternary mirror 4.

Table 1 specifies, and Figures 3A-F show the results of a computed simulation of the performance of the imaging system 1 00. Figures 3A-D show the geometrical ray distribution, not including diffraction, of the image of a stellar source at several field angles up to 0.5° off-axis, superimposed on a circle representing the diameter of the diffraction Airy Disc for a wavelength of 550nm. Figure 3E shows the fraction of the enclosed energy as a function of the radius of the diffracted blur spot image of a stellar source. At a two metre pupil size, the results show that the imaging system 100 of the present invention is diffraction-limited out to half a degree from the axis. Figure 3F shows the distribution of light in the image of a stellar source, including diffraction effects, for the 500mm pupil diameter system, at field angles 0°, 0.2°, 0.4° and 0.5° off-axis. The base of each 2D histogram is 1 5 micrometres square.

Table 7 - Physical Characteristics of a 1m Diameter System

Example 2

In example 2 and in examples 3 and 4, any characteristics of the imaging system that are not stated as differing from example 1 may be assumed to be the same as example 1 , where appropriate.

For larger systems, for example systems with a diameter exceeding 1 m, high order aberrations may begin to detract from image quality. More complex aspheric forms may be superimposed over the surface of any or all of the mirrors to correct for such aberrations and maintain high image quality. However, it is preferred not to add complexity to the convex secondary mirror curve as this may render fabrication and testing excessively difficult.

Table 2 shows the prescription for the design according to this example, which is shown diagrammatically in Figure 4 and generally referenced by arrow 200. In Figure 4 and in Figures 6 and 8, corresponding components of the imaging system 200, 300 or 400 respectively to those in the imaging system 1 00 are indicated by like numerals.

The imaging system 200 has the same general form as imaging system 1 00, but has added aspheric terms to the function defining the curve of the tertiary mirror 3. This enables the pupil diameter to be increased to 2m, while retaining diffraction-limited performance up to 0.3° off-axis. The system aperture stop is located at the plane of the primary mirror and the system has a 0.6° field.

Table 2 - Physical Characteristics of a 2m Diameter System

Figures 5A-D show the distribution of light in the image of a stellar source, including diffraction effects, for the 2m pupil diameter system, at field angles 0°, 0 1 5°, 0.25° and 0.3° off-axis The base of each 2D histogram is 1 5 micrometres square.

Figure 5E shows the fraction of the enclosed energy as a function of the radius of the diffracted blur spot image of a stellar source.

Figure 5F shows the geometrical ray distribution, not including diffraction, of the image of a stellar source at several field angles up to 0.3° off-axis, superimposed on a circle representing the diameter of the diffraction Airy Disc for a wavelength of 550nm.

Example 3

Adding aspheric terms to the prescription of the curve of the primary mirror, enables even greater control of residual aberrations. In this example, the control has been applied to the design of an Extreme Ultra Violet optic, using a wavelength of 100nm. At f/2.4 the diffraction Airy Disc is only 0.586 micrometres diameter, requiring exceptional aberration control in order to achieve a useful field angle.

Table 3 is the prescription for this design, and Figure 6 shows a diagrammatic representation of the imaging system 300, which again has the general form illustrated in Figure 2. The field angle is ±0.5°, as in Example 1 and the pupil diameter is 1 m. The aperture stop of the system is located in the plane of the primary mirror and the system has a 1 .0° field and optimised for a wavelength of 100nm.

A further baffle 5B is shown in Figure 6 around the secondary mirror 2. This further baffle may also be included in examples 1 , 2 and 4 if required. Furthermore, the baffle 5 may be extended further in front of the primary mirror 1 to provide improved baffling if required.

Table 3 - Physical Characteristics of a 1m Diameter System

Figures 9A-D show the distribution of light in the image of a stellar source, including diffraction effects, for the 1 m pupil diameter system, at field angles 0°, 0.2°, 0.4° and 0.5° off-axis. The base of each 2D histogram is 1 .5 micrometres square

Figure 9E shows the fraction of the enclosed energy as a function of the radius of the diffracted blur spot image of a stellar source.

Figure 9F shows the geometrical ray distribution, not including diffraction, of the image of a stellar source at several field angles up to 0.5° off-axis, superimposed on a circle representing the diameter of the diffraction Airy Disc for a wavelength of 1 00nm.

Example 4

In some applications, for example the computation from the image of super-resolution, it is advantageous for the pupil of the imaging system to be of constant format with field angle. In the Examples 1 , 2 and 3 above, this is not the case, because the central obstruction of the secondary, tertiary and quaternary mirrors 2, 3, 4 that obtrude into the light path, is not consistently central in the pupil with off-axis field angles. To reduce the eccentricity of the central obstruction to zero for all field angles, it is necessary that the aperture stop, which is also the entrance pupil of these examples, be located at the same axial position as the periphery of the secondary mirror 2 (assuming that this is the outer periphery of the central obstruction) . Also, the obscuration of the tertiary and quaternary mirrors 3, 4 should completely be enclosed by the obscuration of the secondary mirror 2.

The imaging system 400 as shown in Figure 8 has been computed as a variation of Example 3 to satisfy these requirements. Table 4 is the prescription for this design which has the general form illustrated in Figure 2. The field angle is ±0.5°, as in Examples 1 and 3. The diameter of the entrance pupil of the system is 1 m, and it is positioned in the optical path before the primary mirror, adjacent to the physical location of the secondary mirror, by the existence of an aperture stop formed at the from of the light baffle 5. The aberration correction in this example is the same as for Example 3, and is suited to Extreme Ultra Violet light of 100nm.

Figures 9A-D show the distribution of light in the image of a stellar source, including diffraction effects, for the 1 m pupil diameter system, at field angles 0°, 0.2°, 0.4° and 0.5° off-axis. The base of each 2D histogram is 1 .5 micrometres square.

Figure 9E shows the fraction of the enclosed energy as a function of the radius of the diffracted blur spot image of a stellar source. Figure 9F shows the geometrical ray distribution, not including diffraction, of the image of a stellar source at several field angles up to 0.5° off-axis, superimposed on a circle representing the diameter of the diffraction Airy Disc for a wavelength of 100nm.

Table 4 - Physical Characteristics of a 2m Diameter System

Aperture stop at surface 1

Larger pupil diameters

The design of the present invention lends itself to extension to much larger pupil diameters than those given in the examples 1 -4, at the expense of field angle. Figure 7 shows the relationship between angular field and pupil diameter for a quality of image represented by the Strehl Ratio of 0.9. This represents an image quality from a stellar source virtually indistinguishable from a perfect diffraction-limited image.

This graph was computed by setting each pupil diameter and adjusting the field angle such that, employing the standard least-squares optimisation method, the image quality at the outermost field angle achieved a Strehl Ratio of 0.9 It can be seen that even at 1 km pupil diameter, there is still a useful field angle

Thus, there is provided an imaging system which provides high quality diffraction-limited imaging while having a compact design. Therefore, the imaging system of the present invention may find particular application to imaging operations in space. In addition, those skilled in the art may apply the present invention to the projection of light, in which case the optical path is reversed.

Where in the foregoing description, reference has been made to specific components or integers of the invention having known equivalents then such equivalents are herein incorporated as if individually set forth.

Although this invention has been described by way of example and with reference to possible embodiments thereof, it is to be understood that modifications or improvements may be made thereto without departing from the scope of the invention as defined in the appended claims.

Claims

Claims:

1 An imaging system including a primary, secondary, tertiary and quaternary mirror arranged in a single-axis, double-pass, four reflection format, wherein the quaternary mirror is an aspheric reflecting element.

2. An imaging system as claimed in claim 1 , wherein the primary, secondary and tertiary mirrors are collectively arranged in a Cassegrain-hke format.

3. An imaging system as claimed in either claim 1 or claim 2, wherein the primary and tertiary mirrors are monolithic.

4. An imaging system as claimed in any one of the preceding claims, wherein the primary, secondary and tertiary mirrors have a reflecting surface that is substantially hyperboloidal.

5. An imaging system as claimed in any one of the preceding claims, wherein the tertiary mirror includes an aspheric form superimposed on its surface to reduce aberrations in an image and the primary and secondary mirrors do not have a superimposed aspheric form.

6. An imaging system as claimed in any one of claims 1 to 4, wherein the tertiary mirror and the primary mirror both include an aspheric form superimposed on their respective reflecting surfaces to reduce aberrations in an image and the secondary mirrors does not include a superimposed aspheric form.

7. An imaging system as claimed in any one of the preceding claims, wherein the quaternary mirror has a radius of curvature substantially greater than the radius of curvature of the primary, secondary and tertiary mirrors.

8. An imaging system as claimed in any one of the preceding claims, wherein the quaternary mirror has a radius of curvature tending towards infinity relative to the curvature of the primary, secondary and tertiary mirrors.

9. An imaging system as claimed in any one of the preceding claims, wherein the physical length of the imaging system is approximately equal to or less than the diameter of the entrance pupil.

1 0. An imaging system as claimed in any one of the preceding claims, wherein the quaternary mirror is adapted to reduce aberrations in the image.

1 1 .An imaging system as claimed in any one of the preceding claims, wherein the quaternary mirror is adapted to provide zonal corrections to the image.

1 2. An imaging system as claimed in any one of the preceding claims, further including a baffle extending from the periphery of the primary mirror towards or past the secondary mirror.

1 3. An imaging system as claimed in any one of the preceding claims, including a baffle located centrally of the tertiary mirror and about the image focal point of the imaging system.

14. An imaging system as claimed in any one of the preceding claims, including an aperture stop located substantially at the physical location of the primary mirror.

1 5 An imaging system as claimed in any one of claims 1 to 1 3, including an aperture stop located substantially in a plane coterminous with the secondary mirror.

1 6. An imaging system as claimed in any one of the preceding claims, wherein the relative diameters and location of the primary, secondary, tertiary and quaternary mirrors are such that in use only the secondary mirror acts to obscure the central part of the pupil at any field angle.

1 7. An imaging system as claimed in any one of the preceding claims having a speed faster than or equal to f/2.5.

1 8. An imaging system substantially as herein described and with reference to Figure 2, Figure 4, Figure 6 or Figure 8 of the accompanying drawings.

1 9. An imaging system substantially as herein described and with reference to Figure 2, Figure 4, Figure 6 or Figure 8 of the accompanying drawings and having a performance substantially as defined in one of Figure 3, Figure 5, Figure 7 or Figure 9.

20. A method of imaging light onto an image detecting means including: - receiving incident light by a primary mirror; reflecting light from said primary mirror using a secondary mirror; reflecting light from said secondary mirror using a tertiary mirror located substantially on a common axis to said primary and secondary mirrors; reflecting light from said tertiary mirror using an aspheric quaternary mirror located substantially on said common axis; and receiving light from said quaternary mirror by an image detecting means.

A method of designing an imaging system that includes a primary, secondary, tertiary and quaternary mirror in a single-axis, double- pass, four reflection format, the method including computing an imaging solution that satisfies a set of predetermined criteria using an optimisation algorithm that includes as variables: the relative location and curvature of said primary, secondary, tertiary, and quaternary mirror along said axis; and the structure of an aspheric form superimposed over said quaternary mirror.

22. The method of claim 20, including using the structure of an aspheric form superimposed over said tertiary mirror as a further variable.

23. The method of claim 20 or claim 21 , including using the structure of an aspheric form superimposed over said primary mirror as a further variable.

24. The method of any one of claims 20 to 22, wherein the radius of curvature of the quaternary mirror is constrained so that the quaternary mirror is substantially planar relative to the primary, secondary and tertiary mirrors.

25. The method of any one of claims 20 to 22, wherein the radius of curvature of the quaternary mirror is infinite.

26. An imaging system designed in accordance with the method of any one of claims 20 to 24.

27. A method of designing an imaging system substantially as herein described and with reference to Figures 2 to 1 0.